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  • Aswath Damodaran 1

    Valuation Inferno: Dante meets DCF

    Abandon every hope, ye who enter hereAswath Damodaran

    www.damodaran.com

  • Aswath Damodaran 2

    DCF Choices: Equity versus Firm

    Assets Liabilities

    Assets in Place Debt

    Equity

    Fixed Claim on cash flowsLittle or No role in managementFixed MaturityTax Deductible

    Residual Claim on cash flowsSignificant Role in managementPerpetual Lives

    Growth Assets

    Existing InvestmentsGenerate cashflows todayIncludes long lived (fixed) and

    short-lived(working capital) assets

    Expected Value that will be created by future investments

    Equity valuation: Value just the equity claim in the business by discounting cash flows to equity at the cost of equity

    Firm Valuation: Value the entire business by discounting cash flow to the firm at cost of capital

  • Aswath Damodaran 3

    The Value of a business rests on..

  • Aswath Damodaran 4

    Cashflow to FirmEBIT (1-t)- (Cap Ex - Depr)- Change in WC= FCFF

    Expected GrowthReinvestment Rate* Return on Capital

    FCFF1 FCFF2 FCFF3 FCFF4 FCFF5

    Forever

    Firm is in stable growth:Grows at constant rateforever

    Terminal Value= FCFF n+1/(r-gn)FCFFn.........

    Cost of Equity Cost of Debt(Riskfree Rate+ Default Spread) (1-t)

    WeightsBased on Market Value

    Discount at WACC= Cost of Equity (Equity/(Debt + Equity)) + Cost of Debt (Debt/(Debt+ Equity))

    Value of Operating Assets+ Cash & Non-op Assets= Value of Firm- Value of Debt= Value of Equity

    Riskfree Rate :- No default risk- No reinvestment risk- In same currency andin same terms (real or nominal as cash flows

    + Beta- Measures market risk XRisk Premium- Premium for averagerisk investment

    Type of Business

    Operating Leverage

    FinancialLeverage

    Base EquityPremium

    Country RiskPremium

    DISCOUNTED CASHFLOW VALUATION

  • Aswath Damodaran 5

    The nine circles of valuation hell.. With a special bonus circle

  • Aswath Damodaran 6

    Illustration 1: Base Year fixation.

    You are valuing Exxon Mobil, using the financial statements of the firm from 2007. The following provides the key numbers:Revenues $377 billionEBIT (1-t) $ 42 billionNet Cap Ex $ 3 billionChg WC $ 1 billion

    The cost of capital for the firm is 8% and you use a very conservative stable growth rate of 2% to value the firm. The market cap for the firm is $466 billion and it has $ 9 billion in debt outstanding. a. How under or over valued is the equity in the firm?b. Would you buy the stock based on this valuation? Why or why not?

  • Aswath Damodaran 7

    Normalization not easy to do but

  • Aswath Damodaran 8

    Vale: A Case for Normalization?Year 2004 2005 2006 2007

    Revenues $27,544 $33,993 $45,291 $64,764 Operating Income $10,857 $14,854 $20,088 $29,315 Net Income $6,460 $10,443 $13,431 $20,006 Earnings per share $1.40 $2.27 $2.78 $4.14 CRB Metals Index 357.69 440.85 693.88 811.85

    Deflated Revenues $27,544.00 $27,580.71 $23,347.18 $28,534.13

    1. If you use current earnings as your base, are you likely to find the firm to be under or over valued?

    2. Would you normalize earnings?3. If so, how would you do it?

  • Aswath Damodaran 9

    Embraer: A case for normalization?

    2003 2004 2005 2006 2007 TotalRevenues R$ 6,571 R$ 10,231 R$ 9,133 R$ 8,342 R$ 9,983 R$ 44,260EBIT R$ 1,243 R$ 1,740 R$ 794 R$ 546 R$ 527 R$ 4,850Operating Margin 18.92% 17.01% 8.69% 6.55% 5.28% 10.96%

    Three ways to normalize:1. Average operating income between 2003-2007 = R$ 970 million2. Average operating margin between 2003-2007 = 10.96% -> Applied to

    current revenues of R$9,983 million yields R$ 1,094 million3. Apply industry average margin of 10.68% (US aerospace & defense) to

    current revenues of R$9,983 million yields R$ 1,066 million.

  • Aswath Damodaran 10

    Illustration 2: Taxes and Value

    Assume that you have been asked to value a company and have been provided with the most recent years financial statements:

    EBITDA 140- DA 40EBIT 100- Interest exp 20Taxable income 80Taxes 32Net Income 48Assume also that cash flows will be constant and that there is no growth in

    perpetuity. What is the free cash flow to the firm?

  • Aswath Damodaran 11

    Lesson 2.1: Dont double count the tax benefit

    Taxes paid: When computing the after-tax operating income, using taxes paid (24) will give you a higher cash flow but will result in double counting the tax benefit - once in the cash flow and again in the cost of capital (when you use the after-tax cost of debt)

    Cap Ex:Though nothing is mentioned about cap ex, the fact that these earnings can be maintained in perpetuity requires us to be consistent in our reinvestment assumptions. If you do not set cap ex = depreciation, the assets of the firm will deplete over time to zero but earnings will continue at current levels.

    Ignoring a relevant variable, because you are not given the facts or feel uncertain about it, is just as much an assumption (and often less defensible and more dangerous) than making an explicit assumption.

  • Aswath Damodaran 12

    2.2: Dueling Tax RatesVale Embraer Gerdau Petrobras

    Operating income $29,315.00 $527.00 $4,796.00 $36,432.00 Interest expense $806.00 $276.00 $0.00 $2,160.00 Taxable Income $28,646.00 $828.00 $5,295.00 $34,528.00 Taxes paid $7,086.00 $162.00 $970.00 $11,273.00 Effective tax rate 24.74% 19.57% 18.32% 32.65% Taxes/ EBIT 24.17% 30.74% 20.23% 30.94% Marginal tax rate 34% 34% 34% 34%

    1. Why is the effective tax rate different from the marginal tax rate?2. Why is the effective tax rate different from taxes as a % of EBIT?3. Which tax rate should you use in computing your after-tax operating income?

  • Aswath Damodaran 13

    Illustration 3: High Growth for how long

    Assume that you are valuing a young, high growth firm with great potential, just after its initial public offering. How long would you set your high growth period?

    < 5 years 5 years 10 years >10 years

  • Aswath Damodaran 14

    Lesson 3.1: Maintaining high growth is difficult

    While analysts routinely assume very long high growth periods (with substantial excess returns during the periods), the evidence suggests that they are much too optimistic. A study of revenue growth at firms that make IPOs in the years after the IPO shows the following:

  • Aswath Damodaran 15

    Lesson 3.2: Scaling up growth is hard to do..

  • Aswath Damodaran 16

    You be the judge: How long a growth period?

    Given that growth becomes more difficult to maintain as firms get larger and the market stagnates, what type of growth period would you assign the following firms?

    Embraer: 0 years, 5 years, 10 years, > 10 years Vale: 0 years, 5 years, 10 years, > 10 years Petrobras: 0 years, 5 years, 10 years, > 10 years Gerdau Steel: 0 years, 5 years, 10 years, > 10 years

  • Aswath Damodaran 17

    Illustration 4: Regression betas and Debt Cost

    The US $ cost of capital for Embraer has been computed using the following inputs: The cost of equity was estimated from the ten-year dollar denominated Brazilian

    government bond rate of 6%, a Bloomberg adjusted beta for the Embraer ADR of 1.01 and an equity risk premium for Brazil of 6.2% (based on the US historical risk premium of 4% and an additional risk premium of 2.2% for Brazil.

    Cost of equity = Brazilian Government Bond rate + Beta * Risk Premium

    = 6% + 1.01 (6.2%) = 12.26%

    The cost of debt was computed by dividing the interest expenses (276 mil R$) by the book value of debt (3,127 mil R$); the effective tax rate for the firm is 19.5%.

    Cost of debt = Interest expenses/ Book Debt = 276/ 3127 = 8.82% After-tax cost of debt = Cost of debt (1- Effective tax rate) = 8.82% (1-.195) = 7.10%

    The cost of capital was computed using the market value of equity(12729 million R$) and the book value of all liabilities (10260) as weights for debt and equity

    Cost of capital = 13.87% (12729/(12729+10260)) + 7.1% (10260/(12729+10260)) = 9.96% Do you agree with the computation?

  • Aswath Damodaran 18

    4.1: Government bonds are not always riskless..

    0.00%

    2.00%

    4.00%

    6.00%

    8.00%

    10.00%

    12.00%

    US T Bond Mexican $ Brazilian $ Columbian $ Chilean $ Venezuelan $

    Peru $ Argentine $ Brazilian R$

    Government Bond rate

    These are all US dollar denominated. Why are the rates different?

    R$ rate. Local currency rating is A3., with default spread of 0.85%

  • Aswath Damodaran 19

    4.2: Betas dont come from regressions..

  • Aswath Damodaran 20

    But from a firms business mix as well as operating and financing choices

    Beta of Firm (Unlevered Beta)

    Beta of Equity (Levered Beta)

    Nature of product or service offered by company:Other things remaining equal, the more discretionary the product or service, the higher the beta.

    Operating Leverage (Fixed Costs as percent of total costs):Other things remaining equal the greater the proportion of the costs that are fixed, the higher the beta of the company.

    Financial Leverage:Other things remaining equal, the greater the proportion of capital that a firm raises from debt,the higher its equity beta will be

    Implications1. Cyclical companies should have higher betas than non-cyclical companies.2. Luxury goods firms should have higher betas than basic goods.3. High priced goods/service firms should have higher betas than low prices goods/services firms.4. Growth firms should have higher betas.

    Implicati